Nonlinear oscillation of second order differential equations with state-dependent delays (Q2379041)

The following second order differential equation \[ (r(t)|y{^{\prime}}(t)|^{p-1}y{^{\prime}}(t)){^{\prime}} + f(t,y(t),y(\Delta (t,y(t))))=0 \] is considered, where \(p>0\), \(r \in C[0,\infty)\), \(r(t)>0\) on \([0,\infty)\), \(\int_0^\infty [r(s)]^{-1/p} \,ds< \infty\), \(f \in C([0,\infty) \times\mathbb R^2)\), \(\Delta\in C([0,\infty) \times \mathbb R)\), and there exist \(\Delta_*\), \(\Delta^* \in C[0,\infty)\) such that \(\lim_{t\to\infty} \Delta_*(t)=\infty\) and \(\Delta_*(t) \leq \Delta(t,y) \leq \Delta^*(t) \leq t\) for \(t \geq T\) and \(y \in \mathbb R\). Oscillation and nonoscillation criteria are obtained.